Particle image velocimetry measurements of a shock wave/turbulent boundary layer interaction

Particle image velocimetry is used to investigate the interaction between an incident shock wave and a turbulent boundary layer at Mach 2.1. A particle response assessment establishes the fidelity of the tracer particles. The undisturbed boundary layer is characterized in detail. The mean velocity field of the interaction shows the incident and reflected shock wave pattern, as well as the boundary layer distortion. Significant reversed flow is measured instantaneously, although, on average no reversed flow is observed. The interaction instantaneously exhibits a multi-layered structure, namely, a high-velocity outer region and a low-velocity inner region. Flow turbulence shows the highest intensity in the region beneath the impingement of the incident shock wave. The turbulent fluctuations are found to be highly anisotropic, with the streamwise component dominating. A distinct streamwise-oriented region of relatively large kinematic Reynolds shear stress magnitude appears within the lower half of the redeveloping boundary layer. Boundary layer recovery towards initial equilibrium conditions appears to be a gradual process.     

The accuracy of tomographic particle image velocimetry for measurements of a turbulent boundary layer

To investigate the accuracy of tomographic particle image velocimetry (Tomo-PIV) for turbulent boundary layer measurements, a series of synthetic image-based simulations and practical experiments are performed on a high Reynolds number turbulent boundary layer at Re_θ = 7,800. Two different approaches to Tomo-PIV are examined using a full-volume slab measurement and a thin-volume “fat” light sheet approach. Tomographic reconstruction is performed using both the standard MART technique and the more efficient MLOS-SMART approach, showing a 10-time increase in processing speed. Random and bias errors are quantified under the influence of the near-wall velocity gradient, reconstruction method, ghost particles, seeding density and volume thickness, using synthetic images. Experimental Tomo-PIV results are compared with hot-wire measurements and errors are examined in terms of the measured mean and fluctuating profiles, probability density functions of the fluctuations, distributions of fluctuating divergence through the volume and velocity power spectra. Velocity gradients have a large effect on errors near the wall and also increase the errors associated with ghost particles, which convect at mean velocities through the volume thickness. Tomo-PIV provides accurate experimental measurements at low wave numbers; however, reconstruction introduces high noise levels that reduces the effective spatial resolution. A thinner volume is shown to provide a higher measurement accuracy at the expense of the measurement domain, albeit still at a lower effective spatial resolution than planar and Stereo-PIV.     

Investigation of a compressible turbulent boundary layer and a region of separation at M=5 by a laser Doppler anemometer

Results are cited of an experimental investigation of the structure of a compressible turbulent boundary layer on a thermally insulated cylinder placed longitudinally in the flow. The experiments were conducted at M=5 and Re_x10⁷. In order to establish a longitudinal positive pressure gradient and a region of separation at the end of the cylinder, a tailpiece in the shape of an axisymmetric isentropic compression surface, or conical flaps with various half angles, were mounted. Profiles of the longitudinal velocity component were measured using p_o' and t_o probes, and also using a laser Doppler anemometer (LDA) with a Fabry-Perot interferometer. In the absence of a longitudinal pressure gradient the velocity profiles measured by the different methods were in satisfactory agreement among themselves and with the results of calculations. In the presence of a longitudinal positive pressure gradient, the velocity profiles become less filled and the static pressure, calculated according to the results of measurements of the velocity with the aid of the LDA and the pressure p_o', varied across the thickness of the boundary layer. In the separated region, the recirculating velocity of the flow was measured with the aid of the LDA.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 175–178, March–April, 1976.     

Assessment of turbulent spectral bias in laser Doppler velocimetry

A critical evaluation is made of the spectral bias which occurs in the use of a laser Doppler velocimeter (LDV). In order to accommodate the randomly sampled LDV data, statistical treatments of particle arrival times are needed. This is modeled as a doubly stochastic Poisson process which includes the intensity function of the velocity field. Three processing algorithms are considered for spectral estimates: the sample and hold method (SH), the modified Shannon sampling technique (SR), and the direct transform (RG). Assessment is made of these for varying data densities (0.05 ≤ d.d ≤ 5) and turbulence levels (t.i.=30%, 100%). The effects of the values of the Reynolds stress coefficients and the transversal standard deviation on the spectral contents were examined. As an improved version of the spectral estimator, the utility of POCS (the projection onto convex sets) has been tested in the present study. This algorithm is found useful to be in the region when d.d. ? 3.     

Stability of a compressible boundary layer

The problem of stability in a compressible boundary layer, as opposed to an incompressible layer, involves many parameters and requires consideration of three-dimensional perturbations. The transverse component of the velocity, the thermal regime at the wall, etc., take on great significance. Investigation of all aspects of this problem requires systematic calculations performed by electronic computers. There do exist a few calculations of stability of a compressible boundary layer with respect to three-dimensional disturbances for particular cases. It follows from those studies (see, for example, [1]) that consideration of three-dimensional perturbations and of the transverse component of the basic flow velocity is important. Many aspects of this problem remain uninvestigated. Aside from the sheer cumbersomeness of the problem, there exist purely mathematical difficulties connected with the presence of a small parameter with higher derivatives in the differential equations for the perturbations, which causes losses in accuracy of calculation. In this present study an algorithm will be developed for solution of the problem of stability of a compressible boundary layer relative to three-dimensional disturbances with consideration of the transverse component of the basic velocity. Calculations are performed for a boundary layer on a plane thermally insulating plate, and the effects of the transverse velocity component and the three-dimensionality of the perturbations on stability at various Mach numbers are demonstrated.     

Investigation of a compressible turbulent boundary layer in the presence of tangential blowing and a positive pressure gradient

The present study is devoted to the computational investigation of the compressible turbulent boundary layer and flow that are formed during tangential blowing of various gases in a thick boundary layer for large positive pressure gradients. Such flows occur in elements of the gas-dynamic channel of turbojet engines and liquid-fuel rocket engines, ejector pumps, and other technical devices. Using a numerical method we investigate the effect of various factors (the Mach number of blowing, the type of blown gas, and the intensity of variation of the pressure gradient) on the stability of the boundary layer up to its separation.     

PIV-based pressure fluctuations in the turbulent boundary layer

The unsteady pressure field is obtained from time-resolved tomographic particle image velocimetry (Tomo-PIV) measurement within a fully developed turbulent boundary layer at free stream velocity of U _???=?9.3?m/s and Re_???=?2,400. The pressure field is evaluated from the velocity fields measured by Tomo-PIV at 10?kHz invoking the momentum equation for unsteady incompressible flows. The spatial integration of the pressure gradient is conducted by solving the Poisson pressure equation with fixed boundary conditions at the outer edge of the boundary layer. The PIV-based evaluation of the pressure field is validated against simultaneous surface pressure measurement using calibrated condenser microphones mounted behind a pinhole orifice. The comparison shows agreement between the two pressure signals obtained from the Tomo-PIV and the microphones with a cross-correlation coefficient of 0.6 while their power spectral densities (PSD) overlap up to 3?kHz. The impact of several parameters governing the pressure evaluation from the PIV data is evaluated. The use of the Tomo-PIV system with the application of three-dimensional momentum equation shows higher accuracy compared to the planar version of the technique. The results show that the evaluation of the wall pressure can be conducted using a domain as small as half the boundary layer thickness (0.5??₉₉) in both the streamwise and the wall normal directions. The combination of a correlation sliding-average technique, the Lagrangian approach to the evaluation of the material derivative and the planar integration of the Poisson pressure equation results in the best agreement with the pressure measurement of the surface microphones.     

Bubble migration in a turbulent boundary layer

The wall void peaking distribution observed in an upward turbulent bubbly boundary layer along a flat plate is generated by bubbles that move towards the plate, come into contact with the wall and then slide along it. This transverse ‘migration’ has been studied using flow visualization, high speed video and particle tracking techniques to measure the trajectories of mono-disperse air bubbles at very low void fractions. Investigations have been performed at four Reynolds numbers in the range 280 < Re_θ < 3000, covering both the laminar and turbulent regimes, with mono-disperse bubbles of mean equivalent diameter between 2 mm and 6 mm. Lagrangian statistics calculated from hundreds of trajectories show that the migration only occurs in the turbulent regime and for bubble diameters below some critical value: 3.5 mm < d_eqcrit < 4 mm. Above this size (We > 3), the interface deformation is such that bubbles do not remain at the wall, even when they are released at the surface. Also, bubble migration is shown to be non-systematic, to have a non-deterministic character in the sense that trajectories differ significantly, to increase with Reynolds number and to take place on a short time scale. A series of experiments with isolated bubbles demonstrates that these results are not influenced by bubble–bubble interactions and confirm that two-way coupling in the flow is limited. Flow visualizations show that the migration originates with the capture of bubbles inside the large turbulent structures of the boundary layer (‘bulges’). The bubbles begin to move towards the wall as they cross these structures, and the point at which they reach the wall is strongly correlated with the position of the deep ‘valleys’ which separate the turbulent ‘bulges’. The analysis of the mean Lagrangian trajectories of migrating bubbles confirms these observations. Firstly, the average time of migration calculated from these trajectories coincides with the mean transit time of the bubbles across the structures. Secondly, once the trajectories have been scaled by this transit time and the boundary layer thickness δ, they all have the same form in the region y/δ < 0.4, independent of the Reynolds number.     

Low-Reynolds-number effects in a turbulent boundary layer

Low-Reynolds-number effects in a zero pressure gradient turbulent boundary layer have been investigated using a two-component LDV system. The momentum thickness Reynolds number R is in the range 400 to 1320. The wall shear stress is determined from the mean velocity gradient close to the wall, allowing scaling on wall variables of the inner region of the layer to be examined unambiguously. The results indicate that, for the present R range, this scaling is not appropriate. The effect of R on the Reynolds normal and shear stresses is felt within the sublayer. Outside the buffer layer, the mean velocity is more satisfactorily described by a power-law than by a logarithmic distribution.The support of the Australian Research Council is gratefully acknowledged     

Non-contact boundary layer profiler using low-coherence self-referencing velocimetry

A spatially self-referencing velocimetry system based on low-coherence interferometry has been developed. The measurement technique is contactless and relies on the interference between back-reflected light from an arbitrary reference surface and seeding particles in the flow. The measurement location and the flow velocity are measured relative to the reference surface’s location and velocity, respectively. Scanning of the measurement location along the beam direction does not require mechanical movement of the sensor head. The reference surface (which can move or vibrate relative to the sensor head) can be either an external object or the surface of a body over which measurements are to be performed. The absolute spatial accuracy and the spatial resolution only depend on the coherence length of the light source (tens of microns for a superluminescent diode). The prototype is an all-fiber assembly. An optical fiber of arbitrary length connects the self-contained optical and electronics setup to the sensor head. Proof-of-principle measurements in water (Taylor–Couette flow) and in air (Blasius boundary layer) are reported in this paper.     

Kinematics of a turbulent boundary layer

In the article an attempt is made, within the framework of the Navier-Stokes equations, to describe the field of the instantaneous velocities of a liquid in the region of a turbulent flow near the wall. It is assumed that the velocities of the liquid are determined by the field of the eddies arising in regions of ejections under the action of pressure pulses in the region near the wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 34–40, September–October, 1973.     

Instantaneous, three-component planar Doppler velocimetry using imaging fibre bundles

This paper describes a planar Doppler velocimetry (PDV) technique that is capable of measuring the three, instantaneous and time average components of velocity over two spatial dimensions using a single pair of signal and reference cameras. The three views required to obtain three-component velocity information are guided from the collection optics to a single imaging plane using flexible fibre imaging bundles. These are made up of a coherent array of single fibres and are combined at one end as the input plane to the measurement head. Measurements of the velocity field of a rotating disk are used in the development of the technique and initial results of the instantaneous velocity field of a jet are presented.     

LES of the adverse-pressure gradient turbulent boundary layer

We describe large-eddy simulations (LES) of the flat-plate turbulent boundary layer in the presence of an adverse pressure gradient. The stretched-vortex subgrid-scale model is used in the domain of the flow coupled to a wall model that explicitly accounts for the presence of a finite pressure gradient. The LES are designed to match recent experiments conducted at the University of Melbourne wind tunnel where a plate section with zero pressure gradient is followed by section with constant adverse pressure gradient. First, LES are described at Reynolds numbers based on the local free-stream velocity and the local momentum thickness in the range 6560–13,900 chosen to match the experimental conditions. This is followed by a discussion of further LES at Reynolds numbers at approximately 10 times and 100 times these values, which are well out of range of present day direct numerical simulation and wall-resolved LES. For the lower Reynolds number runs, mean velocity profiles, one-point turbulent statistics of the velocity fluctuations, skin friction and the Clauser and acceleration parameters along the streamwise, adverse pressure-gradient domain are compared to the experimental measurements. For the full range of LES, the relationship of the skin-friction coefficient, in the form of the ratio of the local free-stream velocity to the local friction velocity, to both Reynolds number and the Clauser parameter is explored. At large Reynolds numbers, a region of collapse is found that is well described by a simple log-like empirical relationship over two orders of magnitude. This is expected to be useful for constant adverse-pressure gradient flows. It is concluded that the present adverse pressure gradient boundary layers are far from an equilibrium state.